Question

phân tích thành nhân tử\(\left(a+1\right)\left(a+3\right)\left(a+5\right)\left(a+7\right)+15\) 

Answer 1

(a+1)(a+7)(a+3)(a+5)+15

=(a^2+8a+7)(a^2+8a+15)+15

=(a^2+8a+11-4)(a^2+8a+11+4)+15

=(a^2+8a+11)^2 -4^2+15

=(a^2+8a+11)^2 -1

=(a^2+8a+11-1)(a^2+8a+11+1)

=(a^2+8a+10)(a^2+8a+12)

Answer 2

(a+1)(a+7)(a+3)(a+5)+15

=(a^2+8a+7)(a^2+8a+15)+15

=(a^2+8a+11-4)(a^2+8a+11+4)+15

=(a^2+8a+11)^2 -4^2+15

=(a^2+8a+11)^2 -1

=(a^2+8a+11-1)(a^2+8a+11+1)

=(a^2+8a+10)(a^2+8a+12)